The reason why movement matters is that movement is the FIRST element of STRATEGIC WARFARE, the more movement types you and your opponents forces are capable of the greater the strategic depth. This is why RTS games which initially started with all ground units evolved to have large numbers of air units as well as navel units, teleporting units, subterranean units etc. Each additional movement type had a multiplicative effect on strategy. Note that attack/defense types have a similar effect but are capped in a way movement isn't, all units can still engage each other once they have moved into range, but too many attack/defense types make counter-play too much of a guessing game.
Note that we should be allowing each race to use multiple types of FTL, ideally by starting with 1 and then researching a second or third type. If their were enough types of FTL I would even consider starting each race with 2 types, one 'jump' types and one 'contiguous' type. I've brainstormed 10 types so far.
The second factor is to introduce logistical limitations to all FTL, without some cost to move a ship the blob of doom is going to be the default strategy. As soon as moving a ship actually has a resource cost you stop moving any more fleet then you actually need and start keeping strategic reserves. On top of resource costs you can also have opportunity costs by making movement slower, thus any fleet deployment leaves you open in other areas for a long enough time to actually matter because your fleet can't get back quickly to save the day, this also has the knock-on effect of making intelligence on enemy fleet locations more valuable. I would use Energy as the 'fuel' for all FTL (though the method of spending it would vary), an empire would need to stockpile a large amount of energy for an offensive war effort and the cost would limit ones ability to penetrate into enemy territory, which removes much of the burden currently placed on defensive structures.
Fore our current 3 FTL types it would be as follows
Warp - Traditional 'gas-tank' fleets fill up in orbit of a 'fuel depot' from the global energy supply, fleets share fuel giving them a total range, fuel tanks are a part of ship design which allows you to make tanker ships. Going faster lowers fuel efficiency, higher tech improves fuel efficiency, speed and tank capacity.
Lanes - Ships don't carry energy, instead the lane holds it by being 'charged' with energy that is then consumed as ships pass. Charging takes time and can be done by construction ships or charging stations, lanes can be set to be to be automatically recharged. Higher tech allows ships to move faster and for lanes to hold more charge.
WormHoles - The simplest to understand a large lump-sum of energy is just consumed when a hole is opened. Though I would make the cost scale with the number of ships AND the size of the largest ship (think of it as the size of the hole being made) to add some interesting dynamics. Higher tech can increase range, the speed of opening the wormhole and energy efficiency.